If the line tangent to the curve y = f(x) at (5,20) is y = 6x - 10, then what is the limit as h --> 0, f( 5 + h) - f(5)/h ?
The answer is m = 6 but I don't understand why, please show steps, thank you!
The answer is m = 6 but I don't understand why, please show steps, thank you!
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What's the slope of the tangent line? 6, right? That means that this tangent line that has a slope of 6 passes through a point on the curve when the slope of the curve is also 6. Since (f(x + h) - f(x)) / h is the definition of the derivative (as h goes to 0), then it follows that 6 is the answer.